Daily Practice · Higher Plus

June 2020 - Higher Plus 5-a-day

Every Higher Plus sheet published in June 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.

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June 2020

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' June 2020 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in June 2020

The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.

  1. 1st June 2020The probability of winning a game is 4/5. A player expects 8 wins. How many games did they play?
  2. 2nd June 2020On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
  3. 3rd June 2020A rectangle is 29 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
  4. 4th June 2020Work out the coordinates of the turning point of y = x^2 + 4x - 5.
  5. 5th June 2020y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
  6. 6th June 2020In a vector proof you find that vector PQ = 4a - b and vector RS = 16a - 4b. What does this show about PQ and RS?
  7. 7th June 2020A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
  8. 8th June 2020A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
  9. 9th June 2020Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
  10. 10th June 2020Simplify (x^2 - 12x + 32)/(x - 4).
  11. 11th June 2020y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 81.
  12. 12th June 2020A cuboid measures 15 cm by 14 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  13. 13th June 2020A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  14. 14th June 2020On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
  15. 15th June 2020A block has mass 600 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  16. 16th June 2020In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
  17. 17th June 2020A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
  18. 18th June 2020A cuboid measures 7 cm by 9 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  19. 19th June 2020A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  20. 20th June 2020A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
  21. 21st June 2020x = 100 and y = 18, each correct to the nearest whole number. Work out the upper bound of x - y.
  22. 22nd June 2020Make x the subject of 6x + 8 = y(x + 8).
  23. 23rd June 2020y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
  24. 24th June 2020The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
  25. 25th June 2020A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
  26. 26th June 2020On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  27. 27th June 2020A car covers 590 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  28. 28th June 2020Write 7/(x - 5) + 2/(x + 6) as a single fraction.
  29. 29th June 2020y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
  30. 30th June 2020In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.

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